Yes, it's very wrong. I'd advise you to go to Forvo.com to hear the correct pronunciation of чай (it should be "chai", NOT "che"). I've reported it already but don't expect a quick correction anytime soon. It's no fault of the developers, though. It's just that these things take a long time to correct.
There is a lot of variation in how vowels are pronounced depending on the word in Russian. Take the word Время. It is transliterated as vremya but it is typically pronounced as vremye. I think it is one of the hardest aspects of Russian. But I do agree with you that TTS is off at times: take the word Свитер it pronounces it as sviter not as svityr.
Is the word 'с' pronounced as 'es' or does it tag onto the next word, making it sound like "смолоком"? I wonder the same thing with the word 'в'. Sometimes it sounds like 've' while other times it sounds like it just makes the next word start with a 'v' sound, no extra vowel.
@forstore - Many/most European languages do not use supporting verbs like "is" or "do" in the present tense, and some (like Russian) do not use helping verbs (like "was", "had", "did") in the past tense. The entire thought is contained in the verb itself.
Therefore, the English "Do you drink tea?", "Are you drinking tea?", "Have you been drinking tea?" and "You drink tea?" are all expressed in Russian as "Ты пьешь чай?"
"You drink tea with milk?" can either be seeking confirmation of a memory or known preference, perhaps with the expectation that the drinker will want some or it can represent surprise that someone drinks their tea with milk (though it is more rhetorical in this use).
You're right that the form with "do you" is probably better for most uses.